800 Dr. Chree on the Stresses in the Earttis Crust 



that the horizontal pressure may be very considerably less 

 than gph, and so less than the vertical pressure. 



Noticing that rr in (15) is really a vertical stress, it is 

 obvious that the stress systems (15) and (23) are of the same 

 type. The system (23) is the more general, in so far as it 

 does not assume any relationship between the magnitudes of 

 the vertical and horizontal pressures, and does not make the 

 latter necessarily vanish at the upper surface. The material 

 in the Earth's crust thus presents the same elastic conditions 

 as a vertical prism of similar density acted on by gravity, 

 provided the latter be exposed to suitable horizontal pressures 

 whose intensity depends only on the level. 



§ 17. As a numerical example, let us take Mr. Martin's 

 case, where h is twelve miles and p thrice the density of water. 

 Employing these values in (15) or (23), we rind for the 

 vertical pressure at this depth 



— -~ = 36"8 tons weight per square inch. 



Mr. Martin himself speaks of 440 tons, which suggests the 

 omission of 12 in some divisor. Mr. Parsons gives 40 tons 

 as a rough approximation, which agrees substantially with the 

 above estimate. If the prism existed as an isolated pillar, it 

 would, neglecting atmospheric pressures, be free from hori- 

 zontal pressure, and the maximum stress-difference at its 



base would be simply the above value of — zz, or 36'8 tons 

 weight on the square inch. But when the prism forms part 

 of the Earth's crust, horizontal pressures exist; and so long 

 as they are less than gph, the larger they are the smaller is S. 

 If, for example, we supposed the horizontal pressure to be 



given by — 66 in (15) with 7;= 1/4 we should find S reduced 

 to 24*4 tons weight per square inch. 



Comparing (15) and (23) with (29), we see that our rea- 

 soning points to the conclusion that the material at any given 

 depth in the crust, like the material in a gravitating prism, 

 is under the same condition as a short non-gravitating 

 prism over whose flat ends and curved surface there act 

 uniform pressures, equal respectively to the vertical and hori- 

 zontal pressures actually existent at the point in the crust. 

 Thus experiments on a solid prism might supply definite 

 information as to the elastic state of the Earth's crust if rocks 

 were available of the same composition as the more deep- 

 seated material, and the temperature at which the experiments 

 were made was sufficiently high. 



